Related papers: The Hurwitz existence problem and the prime-degree…
The distribution of prime constellations, such as Twin Primes ($p, p+2$), is traditionally analyzed via probabilistic models or analytic sieve theory. While heuristic predictions are accurate, rigorous proofs are obstructed by the "Parity…
This manuscript recounts some of the author's contributions to algebraic and enumerative combinatorics. We have focused on two types of generalizations of bipartite maps, which are bipartite graphs embedded on surfaces. Maps are known to…
The unit commitment problem is a short-term planning problem in the energy industry. Dantzig-Wolfe decomposition is a popular approach to solve the problem. This paper focuses on primal heuristics used with Dantzig-Wolfe decomposition. We…
In this paper, we aim to provide an accessible survey to various formulae for calculating single Hurwitz numbers. Single Hurwitz numbers count certain classes of meromorphic functions on complex algebraic curves and have a rich geometric…
We give an alternative proof of the Hurwitz existence problem for branched covers of $\mathbb{P}^1$ in the case where the number of ramification points equals the number of branch points, that is, where all the ramification profiles are of…
A scarcely known generalization of Goldbach's conjecture introduced by Hardy and Littlewood states that for every pair of (relatively prime) positive integers m1 and m2, every sufficiently large integer n satisfying certain simple…
In this paper we consider, from a computational point of view, the problem of classifying logics within the Leibniz and Frege hierarchies typical of abstract algebraic logic. The main result states that, for logics presented syntactically,…
Richter, Stephan, and Zhang asked whether every nonrecursive many-one degree contains a least finite-one degree. We solve this question in the negative, already within the class of computably enumerable many-one degrees. Positive answers…
We study permutation groups of given minimal degree without the classical primitivity assumption. We provide sharp upper bounds on the order of a permutation group of minimal degree m and on the number of its elements of any given support.…
We present the realization of Hurwitz algebras in terms of 2x2 vector matrices, which maintain the correspondence between the geometry of the vector spaces used in the classical physics and the underlined algebraic foundation of the quantum…
Hurwitz numbers count covers of curves satisfying fixed ramification data. Via monodromy representation, this counting problem can be transformed to a problem of counting factorizations in the symmetric group. This and other beautiful…
We consider surface branch data with base surface the sphere, odd degree d, three branching points, and two partitions of d of the form (2,...,2,1) and (2,...,2,2h+1). If the third partition has length L, this datum satisfies the…
We investigate properties of attainable partitions of integers, where a partition $(n_1,n_2, \dots, n_r)$ of $n$ is attainable if $\sum (3-2i)n_i\geq 0$. Conjecturally, under an extension of the Cohen and Lenstra heuristics by Holmin et.…
This is the second of two papers on the uniform asymptotics for real double Hurwitz numbers with triple ramification. Using the modified tropical correspondence theorem established in the first paper of this series, we introduce a…
We make some progresses on Saxl conjecture. Firstly, we show that the probability that a partition is comparable in dominance order to the staircase partition tends to zero as the staircase partition grows. Secondly, for partitions whose…
In contrast to all other known Ramanujan-type congruences, we discover that Ramanujan-type congruences for Hurwitz class numbers can be supported on non-holomorphic generating series. We establish a divisibility result for such…
We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…
Digital memristive processing-in-memory overcomes the memory wall through a fundamental storage device capable of stateful logic within crossbar arrays. Dynamically dividing the crossbar arrays by adding memristive partitions further…
We consider the bit complexity of computing Chow forms and their generalization to multiprojective spaces. We develop a deterministic algorithm using resultants and obtain a single exponential complexity upper bound. Earlier computational…
Prime numbers, whose properties are important subjects in mathematics, are also fundamental in computer science notably in IT security, Cryptocurrencies as Bitcoin and Blockchain, cryptography, Code theory notably Error detection codes,…